Shortest path algorithms include,

1. Djikstras

2. Bellman-Ford

3. Floyd Warshall

4. Johnsons Algorithm

5. Viterbi algorithm

The Dijkstra's algorithm basically finds the shortest path in a graph,hence used in many fields including computer networking(Routing systems). It also has application in Google maps to find the shortest possible path from one location to other.In Biology, it is used to find the network model in spreading of a infectious disease.